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Reproduction of the BTA:

Depending on the species, Anemones can reproduce sexually or asexually. Sexual reproduction is how most Anemones species reproduce. Sperm and eggs combine and produce free-swimming lava. Successful sexual reproduction happen rarely in aquarium. Actually, researchers at the National Marine Science Centre at Coffs Harbour have bred sea anemones in captivity for the first time in 2005.
Here is a short video showing an anemone releasing sperm into the water:

Asexual reproduction happen regularly in aquarium. It takes place by lateral fission or budding. This means that the Anemone splits itself into two different anemones. Only two of the 10 species that are natural hosts to anemonefishes can reproduce asexually : Entacmaea quadricolor and Heteractis magnifica.

Splitting is often related to stress or feeding habits. Water changes and major changes in
chemistry can cause them to split. My Anemones split quite often in my 150 gallon reef tank. I bought the first one 3 years ago and I now have close to 20 of them. I feed them shrimp daily and change 20% of the water every month.

It is also possible to cut an anemone in half to propagate it artificially. It appears that only anemones that naturally divide will predictably survive this treatment. However, the percentage of success is arguable (many end up with two pieces of one dead anemone). Species that does not split naturally do not have the powers of regeneration strong enough to heal from such trauma.

This technique looks cruel to me. They propagate quite readily just by feeding them so I see no reason to propagate them artificially. Any way, here is a short video of somebody doing it: